1 Introduction
  1.1 Modern Finance:A Brief History
  1.2 Financial Engineering and Computation
  1.3 Financial Markets
  1.4 Computer Technology
 2 Analysis of AlgorithmS
  2.1 Complexity
  2.2 Analysis of Algorithms
  2.3 Description of Algorithms
  2.4 Software Implementation
 3 Basic Financial Mathematics
  3.1 Time Value of Money
  3.2 Annuities
  3.3 Amortization
  3.4 Yields
  3.5 Bonds
 4 Bond Price Volatility
  4.1 Price Volatility
  4.2 Duration
  4.3 Convexity
 5 Term Structure of Interest Rates
  5.1 Introduction
  5.2 Spot Rates
  5.3 Extracting Spot Rates from Yield Curves
  5.4 Static Spread
  5.5 Spot Rate Curve and Yield Curve
  5.6 Forward Rates
  5.7 Term Structure Theories
  5.8 Duration and Immunization Revisited
 6 Fundamental Statistical Concepts
  6.1 Basics
  6.2 Regression
  6.3 Correlation
  6.4 Parameter Estimation
 7 Option Basics
  7.1 Introduction
  7.2 Basics
  7.3 Exchange-Traded Options
  7.4 Basic Option Strategies
 8 Arbitrage in Option Pricing
  8.1 The Arbitrage Argument
  8.2 Relative Option Prices
  8.3 Put-Call Parity and Its Consequences
  8.4 Early Exercise of American Options
  8.5 Convexity of Option Prices
  8.6 The Option Portfolio Property
 9 Option Pricing Models
  9.1 Introduction
  9.2 The Binomial Option Pricing Model
  9.3 The Black-Scholes Formula
  9.4 Using the Black-Scholes Formula
  9.5 American Puts on a Non-Dividend-Paying Stock
  9.6 Options on a Stock that Pays Dividends
  9.7 Traversing the Tree Diagonally
 10 Sensitivity Analysis Options
  10.1 Sensitivity Measures （“The Greeks”）
  10.2 Numerical Techniques
 11 Extensions of Options Theory
  11.1 Corporate Securities
  11.2 Barrier Options
  11.3 Interest Rate Caps and Floors
  11.4 Stock Index Options
  11.5 Foreign Exchange Options
  11.6 Compound Options
  11.7 Path-Dependent Derivatives
 12 Forwards, Futures, Futures Options, Swaps
  12.1 Introduction
  12.2 Forward Contracts
  12.3 Futures Contracts
  12.4 Futures Options and Forward Options
  12.5 Swaps
 13 Stochastic Processes and Brownian Motion
  13.1 Stochastic Processes
  13.2 Martingales（“Fair Games”）
  13.3 Brownian Motion
  13.4 Brownian Bridge
 14 Continuous-Time Financial Mathematics
  14.1 Stochastic Integrals
  14.2 Ito Processes
  14.3 Applications
  14.4 Financial Applications
 15 Continuous-Time Derivatives Pricing
  15.1 Partial Differential Equations
  15.2 The Black-Scholes Differential Equation
  15.3 Applications
  15.4 General Derivatives Pricing
  15.5 Stochastic Volatility
 16 Hedging
  16.1 Introduction
  16.2 Hedging and Futures
  16.3 Hedging and Options
 17 Trees
  17.1 Pricing Barrier Options with Combinatorial Methods
  17.2 Trinomial Tree Algorithms
  17.3 Pricing Multivariate Contingent Claims
 18 Numerical Methods
  18.1 Finite-Difference Methods
  18.2 Monte Carlo Simulation
  18.3 Quasi-Monte Carlo Methods
 19 Matrix Computation
  19.1 Fundamental Definitions and Results
  19.2 Least-Squares Problems
  19.3 Curve Fitting with Splines
 20 Time Series Analysis
  20.1 Introduction
  20.2 Conditional Variance Models for Price Volatility
 21 lnterest Rate Derivative Securities
  21.1 Interest Rate Futures and Forwards
  21.2 Fixed-Income Options and Interest Rate Options
  21.3 Options on Interest Rate Futures
  21.4 Interest Rate Swaps
 22 Term Structure Fitting
  22.1 Introduction
  22.2 Linear Interpolation
  22.3 Ordinary Least Squares
  22.4 Splines
  22.5 The Nelson-Siegel Scheme
 23 Introduction to Term Structure Modeling
  23.1 Introduction
  23.2 The Binomial Interest Rate Tree
  23.3 Applications in Pricing and Hedging
  23.4 Volatility Term Structures
 24 Foundations of Term Structure Modeling
  24.1 Terminology
  24.2 Basic Relations
  24.3 Risk-Neutral Pricing
  24.4 The Term Structure Equation
  24.5 Forward-Rate Process
  24.6 The Binomial Model with Applications
  24.7 Black-Scholes Models
 25 Equilibrium Term Structure Models
  25.1 The Vasicek Model
  25.2 The Cox-Ingersoll-Ross Model
  25.3 Miscellaneous Models
  25.4 Model Calibration
  25.5 One-Factor Short Rate Models
 26 No-Arbitrage Term Structure Models
  26.1 Introduction
  26.2 The Ho-Lee Model
  26.3 The Black-Derman-Toy Model
  26.4 The Models According to Hull and White
  26.5 The Heath-Jarrow-Morton Model
  26.6 The Ritchken-Sankarasubramanian Model
 27 Fixed-Income Securities
  27.1 Introduction
  27.2 Treasury Agency, and Municipal Bonds
  27.3 Corporate Bonds
  27.4 Valuation Methodologies
  27.5 Key Rate Durations
 28 Introduction to Mortgage-Backed Securities
  28.1 Introduction
  28.2 Mortgage Banking
  28.3 Agencies and Securitization
  28.4 Mortgage-Backed Securities
  28.5 Federal Agency Mortgage-Backed Securities Programs
  28.6 Prepayments
 29 Analysis of MOrtgage-Backed Securities
  29.1 Cash Flow Analysis
  29.2 Collateral Prepayment Modeling
  29.3 Duration and Convexity
  29.4 Valuation Methodologies
 30 Collateralized Mortgage Obligations
  30.1 Introduction
  30.2 Floating-Rate Tranches
  30.3 PAC Bonds
  30.4 TAC Bonds
  30.5 CMO Strips
  30.6 Residuals
 31 Modern Portfolio Theory
  31.1 Mean-Variance Analysis of Risk and Return
  31.2 The Capital Asset Pricing Model
  31.3 Factor Models
  31.4 Value at Risk
 32 Software
  32.1 Web Programming
  32.2 Use of The Capitals Software
  32.3 Further Topics
 33 Answers to Selected Exercises
 Bibliography
 Glossary of Useful Notations
 Index